Question: Simplify the following expression: $y = \dfrac{6n + 54}{-18n + 12}$ You can assume $n \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $6n + 54 = (2\cdot3 \cdot n) + (2\cdot3\cdot3\cdot3)$ The denominator can be factored: $-18n + 12 = - (2\cdot3\cdot3 \cdot n) + (2\cdot2\cdot3)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $y = \dfrac{(6)(n + 9)}{(6)(-3n + 2)}$ Dividing both the numerator and denominator by $6$ gives: $y = \dfrac{n + 9}{-3n + 2}$